Data envelopment analysis (DEA) is a technique that uses data to evaluate the relative efficiencies of decision-making units (DMUs). In real life, the collection of crisp data is onerous; some vagueness can occur due to ...

Until now, little investigation has been done to examine the existence and uniqueness of solutions for fractional differential equations on star graphs. In the published articles on the subject, the authors used a star ...

Fractional calculus of complex orders in the complex domain is a rapidly growing field of interest among many mathematicians. While fractional differential equations in real variables have received much attention recently, ...

The authors would like to inform the readers that the conditions of Theorem 2.2 and Theorem 3.1 of Yadav et al. (2024) is not adequate. The statement and proof of Theorems 2.2 and 3.1 of Yadav et al. (2024) have been ...

A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary ...

We propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is ...

Backward Euler for two dimensional Sobolev equation is discussed in this article. We begin by obtaining some basic a priori estimates for the semi-discrete scheme and for the backward Euler approximation. It is proven that ...

This article presents and analyzes a mixed virtual element approach for discretizing parabolic integro-differential equations in a bounded subset of , in addition to the backward Euler approach for temporal discretization. ...

This article develops and analyses a conforming virtual element scheme for the spatial discretization of parabolic integro-differential equations combined with backward Euler’s scheme for temporal discretization. With the ...

The hybridizable discontinuous Galerkin (HDG) method has been applied to a nonlinear parabolic integro-differential equation. The nonlinear functions are considered to be Lipschitz continuous to analyze uniform in time a ...